Publication Date: 1/1/74     Pages: 2     Date Entered: 2/22/84     Title: LIMIT OF ERROR CONCEPTS AND PRINCIPLES OF CALCULATION IN NUCLEAR MATERIALS CONTROL     January 1974     U.S. ATOMIC ENERGY COMMISSION     REGULATORY GUIDE     DIRECTORATE OF REGULATORY STANDARDS     REGULATORY GUIDE 5.18     LIMIT OF ERROR CONCEPTS AND PRINCIPLES     OF CALCULATION IN NUCLEAR MATERIALS CONTROL A. INTRODUCTION     Section 70.51 of Part 70 of Title 10 of the Code of Federal     Regulations requires certain AEC licensees authorized to possess special     nuclear material to calculate statistical limits of error as part of     their material control and accounting procedures for use in assuring     that special nuclear material in their possession is accounted for.     This guide identifies concepts, principles, and referenced methods that     are acceptable to the Regulatory staff for calculating such limits of     error. B. DISCUSSION     Statistical controls are required as an integral part of special     nuclear materials control and accounting systems to assure that     licensees of fuel processing and fuel fabrication facilities effectively     account for the special nuclear material they possess and localize     losses when they occur. A primary statistical indicator of control is     the quantity of material unaccounted for, which is the observed     difference between the amount of material that should be on hand (book     inventory) and the amount of material determined as physically on hand     (ending inventory). Another indicator is an observed shipper-receiver     difference, which results from comparing two independent determinations     of transferred material. Essential to a comprehensive evaluation of the     significance of these indicators are statistical techniques using     associated limits of error for testing whether detected imbalances may     be attributable to measurement error, biases other than those due to     measurement, possible diversions, or other factors.     In the treatment of measurement data, the concept of a systematic     error is important. A systematic error is said to have occurred when     all members of a subset of the measured values are shifted in the same     direction and by the same amount. This shift changes the expected     values of the measurements, and the effect of the shift can therefore be     thought of as a bias. When the shift is itself a random variable     characterized by a mean and variance, various statistical procedures can     be employed to distinguish the random components due to systematic     effects from those due to "purely random" effects. When scrutinizing a     particular measurement procedure, it is imperative to differentiate     between systematic effects which behave like biases and those which are     created by random phenomena. In particular, biases do not "propagate"     in the same way as do random variables.     Subcommittee N15-3 of the American National Standards Institute     (ANSI) Standards Committee N15, Methods of Nuclear Materials Control,     has developed a standard for calculating limits of error. This standard     is designated ANSI N15.16, "Limit of Error Concepts and Principles of     Calculation in Nuclear Materials Control." The limit of error is defined     in 10 CFR Part 70 as the uncertainty component used in constructing a     95% confidence interval associated with a quantity after any recognized     bias has been eliminated or its effect accounted for. Regulatory Guide     5.3, "Statistical Terminology and Notation for Nuclear Materials     Management," dated February 2, 1973, states that limit of error is     construed as the uncertainty component used to construct a 95%     confidence interval and states, in addition, that the uncertainty     component should include systematic as well as random errors. The new     ANSI standard N15.16, however, defines limit of error as twice the     standard deviation of the estimator. This is not consistent with 10 CFR     Part 70 and Regulatory Guide 5.3 since it does not always result in 95%     confidence intervals. C. REGULATORY POSITION     The concepts, principles, and referenced methods for calculating     limits of error contained in the final draft of ANSI N15.16, "Limit of     Error Concepts and Principles of Calculation in Nuclear Materials     Control,"(1) are generally acceptable to the Regulatory staff for use in     nuclear material control and accounting procedures, subject to the     following:     ----------     (1) Copies may be obtained from the Institute of Nuclear Materials     Management, 505 King Ave., Columbus, Ohio 43201, Attn: Mr. H. L. Toy.     ---------- 1. The calculated limits of error defined in Section 3.2 of the     standard should be based on 95% confidence intervals for the estimator,     which must consider the effective degrees of freedom associated with the     estimated variance. 2. Section 4.6 of the standard should be interpreted to mean that     mistakes and blunders arising from the recording, processing, or     reporting of measurement data, whenever they are appropriately     identified, should be excluded from the input to a limit of error     calculation.     6